Exercise 2 By using the method of separable variables prove that the general solution of the ordinary differential equation is 1 3 y'=y-y²y = y(x) > 16, x ER y = y(x)= = 16ex+c x+c (e 2-1)² After characterizing the following differential equation 1 y = ± y' y 3x then prove that its general solution is ,CER. X == 3y¹y = y(x) = 0, x > 0 x²-cx3 2 -,CER.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Exercise 2
By using the method of separable variables prove that the general solution of the ordinary
differential equation
is
1 3
y' =y-y², y = y(x) > 16, x ER
4
y = y(x):
16ex+c
y = +
x+c
(e 2 - 1)²
After characterizing the following differential equation
1
y'
then prove that its general solution is
X
==
3xy= y = y(x) = 0, x > 0
3y'
x²
-,CER.
Cx3
2
,CER.
Transcribed Image Text:Exercise 2 By using the method of separable variables prove that the general solution of the ordinary differential equation is 1 3 y' =y-y², y = y(x) > 16, x ER 4 y = y(x): 16ex+c y = + x+c (e 2 - 1)² After characterizing the following differential equation 1 y' then prove that its general solution is X == 3xy= y = y(x) = 0, x > 0 3y' x² -,CER. Cx3 2 ,CER.
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